Relativistic Perturbations of an Earth Satellite

The inertial frame of reference in the neighborhood of a test body provided by the construction of Fermi normal coordinates is generalized to include the effect of the body's gravitational field. The metric obtained provides a simple physical description of relativistic corrections to the orbital motion of a satellite of the Earth. The main correction is the nonlinear Schwarzschild field of the Earth; in these coordinates there are also three much smaller terms arising from the solar tidal influence.